Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Lee, Jiwoong; Dullerud, Geir E.

doi:10.1137/050627538

Cited by 80 publications

(34 citation statements)

References 36 publications

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“…This means that the resulting equivalent LPV-SS form contains matrices which not only depend on p k but on its time-shifted version as well. This dynamic-dependence has been encountered and analyzed in LPV control synthesis (Lee and Dullerud (2006)), system theory (Tóth (2010)) and identification (Tóth et al (2009)). Using state transformation with dynamic dependence has also been proved to characterize all equivalent LPV-SS representations of a given LPV system (Tóth et al (2011)).…”

Section: A(p) B(p) C(p) D(p)mentioning

confidence: 99%

On The Similarity State Transformation for Linear Parameter-Varying Systems

Kulcsár

Tóth

2011

IFAC Proceedings Volumes

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Similarity state transformations between equivalent State-Space (SS) representations of discrete-time Linear Parameter-Varying (LPV) systems are investigated. Based on previous results, it is known that to characterize all equivalent LPV-SS representations, the statetransformation matrix must depend dynamically on the scheduling variable. However, preserving static dependence of a LPV-SS representation, i.e. characterizing all equivalent SS representation with static dependence, has primary importance both in control and identification. Therefore, first, the state transformation problem is investigated from an algebraic (behavior) point of view, then conditions are developed to guarantee preservation of the static dependence in similarity state transformations. Additional geometric interpretation of the obtained results, together with computational approach to synthesize state-transformations are also developed. An illustrative example is provided to demonstrate the validity of the obtained results.

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Section: A(p) B(p) C(p) D(p)mentioning

confidence: 99%

On The Similarity State Transformation for Linear Parameter-Varying Systems

Kulcsár

Tóth

2011

IFAC Proceedings Volumes

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“…Another body of work which utilizes multiple Lyapunov functions and is of particular interest for us appears in [36], [38], [35], [37]. In these papers, several fundamental control problems (e.g.…”

Section: Contributions and Organizationmentioning

confidence: 99%

“…[32], [13], [15], [36], [38], [35], [37], [30], [29], [20]. Perhaps one of the earliest references is the work on "piecewise quadratic Lyapunov functions" in [32].…”

Section: Contributions and Organizationmentioning

confidence: 99%

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

Ahmadi¹,

Jungers²,

Parrilo³

et al. 2014

SIAM J. Control Optim.

104

133

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Abstract. We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of graphs called path-complete graphs, and show that any such graph gives rise to a method for proving stability of the switched system. This enables us to derive several asymptotically tight hierarchies of semidefinite programming relaxations that unify and generalize many existing techniques such as common quadratic, common sum of squares, path-dependent quadratic, and maximum/minimumof-quadratics Lyapunov functions. We compare the quality of approximation obtained by certain classes of path-complete graphs including a family of dual graphs and all path-complete graphs with two nodes on an alphabet of two matrices. We derive approximation guarantees for several families of path-complete graphs, such as the De Bruijn graphs. This provides worst-case perfomance bounds for path-dependent quadratic Lyapunov functions and a constructive converse Lyapunov theorem for maximum/minimum-of-quadratics Lyapunov functions.

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“…The parailleters of these systems are indexed, and the indices are called the system 1odes. The papers [72,73] focus on the discrete-time domain, and consider the problems of Il iforil exponential stability atid uniform disturbance attenuation for Markovi;ii jump linear systems. I lere uniiformity refers to almtost sire stability and 2-gain of the sequences of modes, called switcliinig sequelices: tha.t are admissible by the automaton which describes the larkov process.…”

Section: 5mentioning

confidence: 99%

Cooperative Networked Control of Dynamical Peer-to-Peer Vehicle Systems

Dullerud¹,

Bullo²,

Féron³

et al. 2007

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The public reporting burden for this collection of information is estimated to average 1 hour per response. including the time for reviewing instructions. searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information. Including suggestions for reducing the burden, to the Department of Defense, Executive Service Directorate (0704-0188). Respondents should be aware that notwithstanding any other provislon of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)Air ABSTRACTThe goal of this MURI center was the development of a rigorous theoretical foundation, and scalable analytical tools and paradigms for construction of networked control for large numbers of autonomous and semi-autonomous air vehicles. The research is specifically aimed at the critical reliability and performance issues facing autonomous vehicle systems which operate in highly uncertain environments, and enables the vehicles to form teams,manage information, and coordinate operations including deployment, task allocation and search. The program produced both the fundamental theory necessary to allow systematic performance analysis, verification and validation of such systems, as well as algorithms for implementation, and design software. Specifically,advances have been made in dynamic deployment and task allocation;verification and hybrid systems; and information management for cooperative control. The activity of the program has had a significant impact on the understanding and designing of large-scale cooperative UAV systems, providing the long-term basis for major new capability, and will more generally enable systematic construction of large-scale robust real-time distributed systems.

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Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Cited by 80 publications

References 36 publications

On The Similarity State Transformation for Linear Parameter-Varying Systems

On The Similarity State Transformation for Linear Parameter-Varying Systems

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

Cooperative Networked Control of Dynamical Peer-to-Peer Vehicle Systems

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